In my experience, valves stick because:
1) There is a build up of fine dirt or residue,
2) The valves are not made from good material, resulting in the plating flaking off or tarnishing easily,
3) The valve casing is dented or mishaped, due to the tubing having been knocked,
4) The player is hooking his/her finger around the valve when not using it,
5) The player is not pushing the valve down correctly, ie: directly from above (and not off to the side0 and with the end of the finger, not half way along.
It may sound odd, but sitting dodgy valves in a glass of Coca Cola for 20mins or so and then giving them a good rinse can strip off any troublesome tarnish.
I've found that a good quality valve oil often sorts out lttle problems. I swear by 'Blue Juice'.
Finally, give the poor teacher a break! If he, indeed, knew nothing about valves, he wouldn't have the job. Trombonists are usually very knowledgable and self-effacing people. I know this 'cos I am one!!!